That metal pipe is probably the cause, but even if it’s not, one thing is for sure: you definitely have a cold area in your wall. That’s why moisture is condensing there. It will be difficult or impossible to get insulation installed around the pipe from the attic. In cases like this, the best option I know of involves injecting spray foam insulation into the cavity around the pipe from inside your bathroom. Start by drilling a series of 3/8″ diameter vertical holes through the wall surface only, every 6 inches from floor to ceiling. Next, buy three or four cans of spray foam and inject it into the cavity through the holes. You’ll need to exercise judgment about how much to apply in each hole, and you should protect the floor in case foam comes out of the holes and drops down as it hardens. Allow any excess foam to harden fully before breaking the chunks off the wall, then remove foam from the injection holes with your drill bit, and finally patch the holes with drywall compound. Assuming there’s even a little space between the pipe and wall surface, foaming will solve the problem.
How can I stop a strip of condensation from forming on one wall of my bathroom during cold weather? It always happens after a shower, and I think it’s caused by a cast iron plumbing vent directly behind the wall surface that goes up through the roof.